Globoid worm gear generating method

ABSTRACT

There is disclosed a globoid worm gear generating method in which the surface of a globoid worm generating tool is defined as the tooth surface of an intermediate gear by an inverted conical surface whose semivertical angle γ is 90°&lt;γ&lt;180°, a relational movement similar to that of a globoid worm wheel is given to the tool so as to generate a globoid worm, and the worm wheel is generated by a wheel generating tool having a contour wholly or partially similar to that of the globoid worm, or in which the surfaces of a globoid worm generating tool are defined wholly or partially by two inverted conical surfaces whose semivertical angles γ are 90°&lt;γ&lt;180°, and the major axes as well as bottoms of the two inverted conical surfaces are coincident with each other so that both tooth surfaces of a worm may be simultaneously generated. By this method of the invention, the globoid worm gears can be generated within a short period of time.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a globoid worm gear generating methodin which tooth surfaces are ground by a tool representing an invertedconical surface.

2. Description of the Prior Art

Hitherto, as methods for generating globoid worm gears, there have beenpublicly known a method in which tooth surfaces of globoid worm gears(globoid worm gears having developable tooth surfaces) are ground andgenerated with a tool representing a plane, a method in which toothsurfaces of globoid worm gears are ground and generated with a toolrepresenting a conical surface (see U.S. Pat. No. 4,184,796) and so on.A comparison will be made between the generating method using the planetool and the generating method using the conical-surface tool. In themethod utilizing the plane tool, the freedom of design is restricted andthere exists a defect that both tooth surfaces of a worm gear cannot begenerated simultaneously. Accordingly, the generating method with theuse of the conical-surface tool has been widely employed at present.

This publicly-known generating method utilizing the conical-surface toolwill now be described. As shown in FIG. 11, a tool 2 rotated by a motor1 has conical surfaces. Both conical surfaces of the tool 2simultaneously generate a globoid worm gear 3.

However, the aforesaid publicly-known worm gear generating method withthe conical-surface tool 2 is not always advantageous in view of cost.This is because it take a long period of time to mill and to grind theworm gears.

A method for generating globoid worm gears with a milling cutter of aninverted conical shape has been proposed (see Japanese Patent UnexaminedPublication No. 2-232119).

This method will be explained with reference to FIG. 12. Rotation of amotor 11 is transmitted to a holder 14 by means of a pulley 12 and abelt 13. A cutting tool 15 for milling is attached to the holder 14. Thecutting tool 15 cuts a globoid worm gear 16 when the holder 14 isrotated.

Such method of cutting the globoid worm gear 16 by the cutting tool 15of the inverted conical shape, has an advantage that a period of timerequired for cutting is shortened. However, the tooth surface of thegear is rough because of the cutting by means of the cutting tool 15, sothat there arises a necessity of finish-grinding the surface with agrindstone. Normally, a difference between a contour of a conicalgrindstone gear made of a conical-surface grindstone for thefinish-grinding and a contour of the threaded gear produced by thecutting tool of the inverted conical shape is large so that a grindingstock is increased. As a result, a period of time of grinding forfinishing the surface of the gear disadvantageously becomes longer afterall.

In view of the above, an object of the present invention resides inproviding a novel method for generating globoid worm gears by which thegears can be generated in a short period of time.

SUMMARY OF THE INVENTION

Characteristics of the present invention exist in the followingstructures.

According to a first aspect of the invention, there is provided a methodfor generating globoid worm gears based on the basic member gear theory,wherein the surface of a globoid worm generating tool is defined as thetooth surface of an intermediate gear wholly or partially by an invertedconical surface whose semivertical angle γ is 90°<γ<180°, a relationalmovement similar to that of a globoid worm wheel is given to the tool soas to generate a globoid worm, and the worm wheel is generated by awheel generating tool having a contour wholly or partially similar tothat of the globoid worm.

According to a second aspect of the invention, there is provided amethod for generating globoid worm gears based on the basic member geartheory, wherein the surfaces of a globoid worm generating tool aredefined as the tooth surfaces of an intermediate gear wholly orpartially by two inverted conical surfaces whose semivertical angles γare 90°<γ<180°, and the major axes as well as bottoms of the twoinverted conical surfaces are coincident with each other so that bothtooth surfaces of a worm gear may be simultaneously generated.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a view showing the relationship between the axes of a worm, awheel and an intermediate gear when the worm gears are generated by aplane tool;

FIG. 2 is a view showing the relationship between the axes of a worm, awheel and an intermediate gear when the globoid worm gears are generatedby a conical-surface tool;

FIG. 3 is a view, on an enlarged scale, showing the relationship betweenthe tooth surface of the intermediate gear shown in FIG. 2 and the axisthereof;

FIG. 4 shows a difference among semivertical angles of the surfaces ofthe worm gear generating tools, in which FIG. 4(A) is a view of theconical-surface tool, FIG. 4(B) is a view of the plane tool, and FIG.4(C) is a view of an inverted conical-surface tool;

FIG. 5 is a view showing the relationship between the axes of a worm, awheel and an intermediate gear when the globoid worm gears are generatedby the inverted conical-surface tool;

FIG. 6 is a view showing the relationship between the tooth surface ofthe intermediate gear shown in FIG. 5 and the axis thereof;

FIG. 7A shows a front view of an example wherein the invertedconical-surface tool is used under such a specific condition that α=0and c=0, and FIG. 7B is a side view of the example;

FIGS. 8A and 8B are views showing positions of tools and worm blankswhen c=0 and α=0, in which FIG. 8A indicates a case of theconical-surface tool and FIG. 8B indicates a case of the invertedconical-surface tool;

FIG. 9(A) shows the tooth profile of the gear generated by theconical-surface tool, FIG. 9(B) shows the tooth profile of the geargenerated by the inverted conical-surface tool and FIG. 9(C) shows adifference between the two tooth profiles;

FIG. 10(A) is a view of the patterns of lines of contact when the gearsare generated by the conical-surface tool, and FIG. 10(B) is a view ofthe same when the gears are generated by the inverted conical-surfacetool;

FIG. 11 is a schematic view for explanation of a globoid worm geargenerating method using a conventional publicly-known conical-surfacetool; and

FIG. 12 is a schematic view of an apparatus for cutting a globoid wormgear with a conventional publicly-known milling cutter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

One embodiment of the present invention will now be described withreference to the drawings.

Prior to the description of the embodiment of the present invention, thegist of the invention will be explained. Taking it into account that aperiod of time of cutting is shortened in case of using theabove-described cutting tool of the inverted conical shape for milling,the present invention aims to generate globoid worm gears with a toolrepresenting an inverted conical-shape.

The present invention will be explained below while adding descriptionsof generating methods with a conventional publicly-known plane tool, aconical-surface tool and a cutting tool of an inverted conical shape formilling, in order to help understanding of the present invention.

At first, a generating method using a plane tool will be explained.

High efficiency of globoid worm gears having developable tooth surfaces,which are based on the basic member gear theory in KIKAI GAKKAI RONBUN(Journal of Japan Society of Mechanical Engineers), 1955, Vol. 21, No.102, Page 164, Sakai as well as the secondary action theory in the same,1972, Vol. 38, No. 311, Page 1895, Sakai and Maki, has been alreadyproved and widely accepted in the art. However, in generating theconventional globoid worm gears having developable tooth surfaces (ofthe type reported in KAKAI GAKKAI KOENSHU RONBUN, Reports in Conferenceheld by Japan Society of Mechanical Engineers, No. 740-15, Sakai andMaki), a tooth surface of an intermediate gear is a plane, and the planeis in parallel with the axis of the intermediate gear. These twoconditions have restricted the freedom of globoid worm gear design.Especially in case of designing low-gear-ratio worm gears, theinconvenience resulting from the conditions is considerable.

In addition, there has been a defect that because of the use of a toolrepresenting a plane (a plane tool), both tooth surfaces of a thread ofa worm cannot be generated simultaneously.

An explanation will now be made of a case in which globoid worm gearsare generated based on the basic member gear theory and the secondaryaction theory.

Referring to FIG. 1, I₁ denotes the axis of a worm; I₂, the axis of awheel; and I₃, the axis of an intermediate gear. In the righthandedcartesian coordinate system O-xyz as an absolute coordinate fixed in thespace, the x-axis corresponds to the axis I₁ ; the z-axis, to the axisI₂ ; and the y-axis, to the perpendicular O₂ O₁ between the axes I₁ andI₂. The axis I₃ intersects at right angles the perpendicular O₂ O₁ at apoint O₃, and makes an angle α to the axis I₂. (O₁ and O₂ denote thepoints of intersection between the perpendicular O₂ O₁ between the axesI₁ and I₂ and the worm axis I₁ and the wheel axis I₂, respectively.)

In the case where angular velocities of the worm axis I₁, the wheel axisI₂ and the intermediate gear axis I₃ are represented by ω₁, ω₂, ω₃, atranslation velocity of the intermediate gear axis I₃ therealong isrepresented by ω₃, rotational ratios i, j, h are expressed by ω₁ /ω₂, ω₁/ω₃, and ω₃ /ω₃ (the ratio h being in term of pitch of screw motion ofthe intermediate gear), a distance between O₂ and O₁ is expressed by e,and a distance between O₃ and O₁ is expressed by e₁, the followingconditions or equations must be satisfied:

    e.sub.1 =e·cos.sup.2 α                      (1)

    j=i·cosα-sinα                         (2)

    h=ω.sub.3 /ω.sub.3 =e·sinα·cosα (3)

Reversely, the tooth surface of a gear cutting tool in any suitableconfiguration is attached to the axis I₃ which satisfies the equations(1) to (3) to machine a worm blank on the axis I₁ and a worm wheel blankon the axis I₂. Then, the line of contact between the worm and wheelcoincides with the line of contact between the intermediate gear andworm (this coincident line of contact is called "the first line ofcontact"). The globoid worm gear generating method described above iscalled the indirect generating method.

Especially, when α=0, the intermediate gear axis I₃ coincides with thewheel axis I₂, and when α=90° the intermediate gear axis I₃ coincideswith the worm axis I₁ so that the intermediate gear may not be takeninto consideration. Thus, the gear generating method in this case iscalled the direct generating method.

Further, according to the "secondary action theory" when a worm wheel isdirectly generated by a generating tool wholly or partially similar inconfiguration to a worm generated by an intermediate gear whichsatisfies the above equations (1), (2) and (3), the worm and worm wheelsimultaneously contact with each other along another line of contact(which is called "the second line of contact") in addition to the firstline of contact. Furthermore, at a point where the worm and worm wheelcontact only one time (to be referred to as "limit normal point"), therelative radius of curvature becomes infinity (∞). In practice the curve(to be referred to as "limit normal point curve") at which it can beexpected that the relative radius of curvature becomes infinity (∞) ispreferably within the zone of contact between the worm and worm wheel sothat there arises a problem how to determine the tooth profile of theintermediate gear.

In the globoid worm gear having developable tooth surfaces, the toothsurface of the intermediate gear is a plane A (a plane tool) in parallelwith the intermediate gear axis I₃ and spaced apart therefrom by adistance a. The employment of this plane results in the advantage thatthe translation of the intermediate gear axis I₃ may be eliminated whenmachining. Furthermore, in respect of efficiency, the limit normal pointcurve can be brought into the zone of contact so that high efficiencyworm gears have been produced.

A globoid worm gear generating method by a tool representing a conicalsurface will be described hereinafter.

The globoid worm gear generating method by the conical-surface tool isalso based on the basic member gear and secondary action theoriesdescribed above. Accordingly, the positional relationships between therespective axes are similar to those in FIG. 1, and the above threeconditions or equations (1), (2) and (3) must be equally satisfied. Inaddition, the essential feature of this method resides in the fact thatthe tool surface of an intermediate gear employs a conical surface (aconical-surface tool) on the basis of these conditions.

As shown in FIG. 2, the tooth surface of an intermediate gear consistsof a conical surface B, and FIG. 3 shows the positional relationshipbetween the axis of the intermediate gear and the tooth surface thereofmore in detail.

The conical surface B which is the tooth surface of the intermediategear has a semivertical angle γ and the major axis O₄ O₅ thereof (O₄being the apex of the cone). The z₃ axis of the righthanded cartesiancoordinate system O₃ -x₃ y₃ z₃ fixed on the intermediate gear axis, theorigin of which is the point O₃, coincides with the axis I₃ of theintermediate gear. The major axis of O₄ O₅ lies in the plane wherein y=band is inclined at an angle δ with respect to the plane x₃ y₃. Thus, thepoint O₅ is the intersection between the major axis O₄ O₅ and parallelplane (Z₃ =-c) to the plane x₃ y₃ and has the coordinates (0, b, -c).And O₄ O₅ =a.

The above-described generating method shown in FIG. 1 can be called agenerating method using a plane tool, and the generating method shown inFIGS. 2 and 3 can be called a generating method using a conical-surfacetool. In a generating method according to the present invention, a toolhaving an inverted conical-surface is utilized in place of theconical-surface tool shown in FIG. 3.

Referring to FIG. 4, the conical-surface tool shown in FIG. 4(A) has asemivertical angle γ larger than 0° and smaller than 90°. The plane toolshown in FIG. 4(B) has a semivertical angle γ of 90°. The invertedconical-surface tool shown in FIG. 4(C) has a semivertical angle γ ofthe conical surface (inverted conical surface) larger than 90° andsmaller than 180°.

Thus, one of characteristics of the invention is that the semiverticalangle y of the tool surface is larger than 90° and smaller than 180°.

A globoid worm gear generating method by the inverted conical-surfacetool according to the invention will be described hereinafter.

The globoid worm gear generating method by the inverted conical-surfacetool is also based on the basic member gear and secondary actiontheories described above. Accordingly, the positional relationshipsbetween the respective axes are similar to those in FIG. 1, and theabove three conditions or equations (1), (2) and (3) must be equallysatisfied. In addition, the essential feature of the present inventionresides in the fact that the tool surface of an intermediate gearemploys an inverted conical surface (an inverted conical-surface tool)on the basis of these conditions.

Referring to FIGS. 5 and 6, the positional relationship of the axes of aworm, a wheel and an intermediate gear in the globoid worm gearaccording to the invention and the relationship between the toothsurface of the intermediate gear and the axis thereof will be describedas follows.

More specifically, similarly to the method using the conical-surfacetool shown in FIGS. 2 and 3, the inverted conical surface C which is thetooth surface of the intermediate gear has a semivertical angle γ andthe major axis O₄ O₅ thereof (O₄ being the apex of the inverted cone).The z₃ axis of the righthanded cartesian coordinate system O₃ -x₃ y₃ z₃fixed on the intermediate gear axis, the origin of which is the pointO₃, coincides with the axis I₃ of the intermediate gear. The major axisO₄ O₅ lies in the plane wherein y₃ =b and is inclined at an angle δ withrespect to the plane X₃ Y₃. Thus, the point O₅ is the intersectionbetween the major axis O₄ O₅ and parallel plane (z₃ =-c) to the plane x₃y₃ and has the coordinates (0, b, -c). And O₄ O₅ =a.

FIGS. 7A and 7B are views showing relationships of relative positionsbetween the inverted conical-surface tool according to the invention andthe worm gear. In this example, c=0, and α=0. When c =0, the major axesof two inverted conical surfaces for generating both right and lefttooth surfaces of a globoid worm coincide with each other so that theymay be generated simultaneously. In addition, when α=0, the axes of theintermediate gear and wheel coincide with each other; that is, thedirect gear generating method.

FIGS. 8A and 8B illustrate positions of the conical-surface tool and theinverted conical-surface tool, respectively when c=0 and α=0. As shownin FIGS. 8A and 8B, the conical-surface tool generates a gear at aportion K in FIG. 8A, while the inverted conical-surface tool generatesa gear at a portion K in FIG. 8B. The portions of the conical-surfacetool and the inverted conical-surface tool used for generating the gearsare clearly different from each other.

Next, a difference in profile of the tooth between the gears generatedby the conical-surface tool and by the inverted conical-surface toolwill be examined on the basis of FIG. 9. FIG. 9(C) shows the differencebetween the tooth profile of the gear generated by the conical-surfacetool shown in FIG. 9(A) and the tooth profile of the gear generated bythe inverted conical-surface tool shown in FIG. 9(B). As seen in FIG.9(C), it is understood that the pressure angles are largely differentfrom each other. This means that a finishing stock (grinding stock) islarge when the gear tooth shape to be be finished by the invertedconical-surface tool is intended to be finished by the conical-surfacetool (grindstone). Accordingly, if the inverted conical-surface tool isused as a finishing tool (grindstone), the grinding stock can beminimized so that a globoid worm can be obtained in a short period oftime of thread chasing and grinding.

If the worm gear generated by the inverted conical-surface tool isinferior in performance to that obtained by the conventionalpublicly-known conical-surface tool, the use of the former tool cannotbe considered to be favorable. However, as shown in FIGS. 10(A) and10(B) which illustrate the pattern of lines of contact in case ofgenerating the worm gear by the conical-surface tool and the pattern oflines of contact in case of generating the worm gear by the invertedconical-surface tool, respectively, the patterns of lines of contact inboth cases almost coincide with each other. Further, as indicated inTable 1, there is little difference in respect of an angle between thedirection of line of contact and a direction of slippage, a relativeradius of curvature and a length of line of simultaneous contact.Therefore, the inverted conical-surface tool according to the inventioncan stand comparison with the conventional publicly-knownconical-surface tool in regard to performance.

                  TABLE 1                                                         ______________________________________                                        COMPARISON OF CONTACT LINE AND RELATIVE                                       RADIUS OF CURVATURE BETWEEN WORM                                              GEARS GENERATED BY CONICAL-SURFACE                                            TOOL AND INVERTED CONICAL-SURFACE TOOL                                                       WORM GEAR   WORM GEAR                                                         GENERATED   GENERATED BY                                                      BY CONICAL- INVERTED                                           ITEM           SURFACE     CONICAL-SUR-                                       OF COMPARISON  TOOL        FACE TOOL                                          ______________________________________                                        ANGLE BETWEEN  75°  68°                                         DIRECTIONS OF                                                                 CONTACT LINE                                                                  AND SLIPPAGE                                                                  RELATIVE RADIUS                                                                              107         107                                                OF CURVATURE (mm)                                                             LENGTH OF LINE OF                                                                             47          50                                                SIMULTANEOUS CON-                                                             TACT (mm)                                                                     ______________________________________                                    

(Calculated under such a condition that a distance between the centersis 100 and a reduction ratio is 80)

As mentioned above, the present invention provides remarkable effectswhich will be described blow.

According to the invention, since a grinding stock is minimized, aperiod of time required for generating the gears can be reduced.Therefore, the invention is significantly effective as a globoid wormgear generating method. Also, the generating method of the invention isnot inferior to a generating method using a conventional conical-surfacetool in respect of performance.

What is claimed is:
 1. A method of generating globoid worm gears basedon the basic member gear theory, comprising the steps of:defining thesurface of a globoid worm generating tool as a tooth surface of anintermediate gear wholly by an inverted conical surface whosesemivertical angle γ is 90°<γ180°; generating a globoid worm by giving arelational movement similar to that of a globoid worm wheel to saidtool; and generating the worm wheel by a wheel generating tool havingcontour wholly similar to that of the globoid worm.
 2. A method ofgenerating globoid worm gears based on the basic member gear theory,comprising the steps of:defining the surface of a globoid wormgenerating tool as a tooth surface of an intermediate gear partially byan inverted conical surface whose semivertical angle γ is 90°<γ<180°;generating a globoid worm by giving a relational movement similar tothat of a globoid worm wheel to said tool; and generating the worm wheelby a wheel generating tool having contour partially similar to that ofthe globoid worm.
 3. A method of generating globoid worm gears based onthe basic member gear theory, comprising the steps of:defining thesurface of a globoid worm generating tool as a tooth surface of anintermediate gear partially by an inverted conical surface whosesemivertical angle γ is 90°21 γ<180°; generating a globoid worm bygiving a relational movement similar to that of a globoid worm wheel tosaid tool; and generating the worm wheel by a wheel generating toolhaving contour wholly similar to that of the globoid worm.
 4. A methodof generating globoid worm gears based on the basic member gear theory,comprising the steps of:defining the surface of a globoid wormgenerating tool as a tooth surface of an intermediate gear wholly by aninverted conical surface whose semivertical angle γ is 90°<γ<180°;generating a globoid worm by giving a relational movement similar tothat of a globoid worm wheel to said tool; and generating the worm wheelby a wheel generating tool having contour partially similar to that ofthe globoid worm.